Strabismus represents a complex oculomotor disorder characterized by the deviation of one or both eyes and poor vision. A more sophisticated understanding of the genetic liability of strabismus is required to guide searches for associated molecular variants. In this classical twin study of 1,462 twin pairs, we examined the relative influence of genes and environment in comitant strabismus, and the degree to which these influences can be explained by factors in common with refractive error. Participants were examined for the presence of latent (‘phoria’) and manifest (‘tropia’) strabismus using cover–uncover and alternate cover tests. Two phenotypes were distinguished: eso-deviation (esophoria and esotropia) and exo-deviation (exophoria and exotropia). Structural equation modeling was subsequently employed to partition the observed phenotypic variation in the twin data into specific variance components. The prevalence of eso-deviation and exo-deviation was 8.6% and 20.7%, respectively. For eso-deviation, the polychoric correlation was significantly greater in monozygotic (MZ) (r = 0.65) compared to dizygotic (DZ) twin pairs (r = 0.33), suggesting a genetic role (p = .003). There was no significant difference in polychoric correlation between MZ (r = 0.55) and DZ twin pairs (r = 0.53) for exo-deviation (p = .86), implying that genetic factors do not play a significant role in the etiology of exo-deviation. The heritability of an eso-deviation was 0.64 (95% CI 0.50–0.75). The additive genetic correlation for eso-deviation and refractive error was 0.13 and the bivariate heritability (i.e., shared variance) was less than 1%, suggesting negligible shared genetic effect. This study documents a substantial heritability of 64% for eso-deviation, yet no corresponding heritability for exo-deviation, suggesting that the genetic contribution to strabismus may be specific to eso-deviation. Future studies are now needed to identify the genes associated with eso-deviation and unravel their mechanisms of action.